{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hierarchical Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hierarchical clustering avoids the need to specify a target number of clusters because it assumes that data can successively be merged into increasingly dissimilar clusters. It does not pursue a global objective but decides incrementally how to produce a sequence of nested clusters that range from a single cluster to clusters consisting of the individual data points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While hierarchical clustering does not have hyperparameters like k-Means, the measure of dissimilarity between clusters (as opposed to individual data points) has an important impact on the clustering result. The options differ as follows:\n",
    "\n",
    "- Single-link: distance between nearest neighbors of two clusters\n",
    "- Complete link: maximum distance between respective cluster members\n",
    "- Group average\n",
    "- Ward’s method: minimize within-cluster variance\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports & Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:38:48.032103Z",
     "start_time": "2018-12-27T18:38:47.706556Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy.cluster.hierarchy import dendrogram, linkage, cophenet\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.cluster import AgglomerativeClustering\n",
    "from sklearn.metrics import adjusted_mutual_info_score\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.datasets import load_iris\n",
    "from matplotlib.animation import FuncAnimation\n",
    "from scipy.spatial.distance import pdist\n",
    "from IPython.display import HTML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:38:48.036198Z",
     "start_time": "2018-12-27T18:38:48.033712Z"
    }
   },
   "outputs": [],
   "source": [
    "# if you have difficulties with ffmpeg to run the simulation, see https://stackoverflow.com/questions/13316397/matplotlib-animation-no-moviewriters-available\n",
    "# plt.rcParams['animation.ffmpeg_path'] = your_windows_path\n",
    "plt.rcParams['animation.ffmpeg_args'] = '-report'\n",
    "plt.rcParams['animation.bitrate'] = 2000\n",
    "\n",
    "sns.set_style('whitegrid')\n",
    "pd.options.display.float_format = '{:,.2f}'.format"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Load Iris Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:38:48.049158Z",
     "start_time": "2018-12-27T18:38:48.037183Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'target_names', 'DESCR', 'feature_names', 'filename'])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris = load_iris()\n",
    "iris.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:38:48.056519Z",
     "start_time": "2018-12-27T18:38:48.050635Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _iris_dataset:\n",
      "\n",
      "Iris plants dataset\n",
      "--------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 150 (50 in each of three classes)\n",
      "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      "        - sepal length in cm\n",
      "        - sepal width in cm\n",
      "        - petal length in cm\n",
      "        - petal width in cm\n",
      "        - class:\n",
      "                - Iris-Setosa\n",
      "                - Iris-Versicolour\n",
      "                - Iris-Virginica\n",
      "                \n",
      "    :Summary Statistics:\n",
      "\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "                    Min  Max   Mean    SD   Class Correlation\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: 33.3% for each of 3 classes.\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\n",
      "from Fisher's paper. Note that it's the same as in R, but not as in the UCI\n",
      "Machine Learning Repository, which has two wrong data points.\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "   - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "     Structure and Classification Rule for Recognition in Partially Exposed\n",
      "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "     on Information Theory, May 1972, 431-433.\n",
      "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "     conceptual clustering system finds 3 classes in the data.\n",
      "   - Many, many more ...\n"
     ]
    }
   ],
   "source": [
    "print(iris.DESCR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Create DataFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:38:48.068285Z",
     "start_time": "2018-12-27T18:38:48.058226Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 150 entries, 0 to 149\n",
      "Data columns (total 5 columns):\n",
      "sepal length (cm)    150 non-null float64\n",
      "sepal width (cm)     150 non-null float64\n",
      "petal length (cm)    150 non-null float64\n",
      "petal width (cm)     150 non-null float64\n",
      "label                150 non-null int64\n",
      "dtypes: float64(4), int64(1)\n",
      "memory usage: 5.9 KB\n"
     ]
    }
   ],
   "source": [
    "features = iris.feature_names\n",
    "data = pd.DataFrame(data=np.column_stack([iris.data, iris.target]), \n",
    "                    columns=features + ['label'])\n",
    "data.label = data.label.astype(int)\n",
    "data.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Standardize Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The use of a distance metric makes hierarchical clustering sensitive to scale:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:38:48.080376Z",
     "start_time": "2018-12-27T18:38:48.069228Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "scaler = StandardScaler()\n",
    "features_standardized = scaler.fit_transform(data[features])\n",
    "n = len(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Reduce Dimensionality to visualize clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:38:48.180503Z",
     "start_time": "2018-12-27T18:38:48.081461Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "pca = PCA(n_components=2)\n",
    "features_2D = pca.fit_transform(features_standardized)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:38:48.312047Z",
     "start_time": "2018-12-27T18:38:48.181677Z"
    },
    "hide_input": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ev1, ev2 = pca.explained_variance_ratio_\n",
    "ax = plt.figure().gca(title='2D Projection', \n",
    "                      xlabel='Explained Variance: {:.2%}'.format(ev1), \n",
    "                      ylabel='Explained Variance: {:.2%}'.format(ev2))\n",
    "ax.scatter(*features_2D.T, c=data.label, s=10);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Perform agglomerative clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:38:48.323761Z",
     "start_time": "2018-12-27T18:38:48.313042Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.01000000e+02, 1.42000000e+02, 0.00000000e+00, 2.00000000e+00],\n",
       "       [7.00000000e+00, 3.90000000e+01, 1.21167870e-01, 2.00000000e+00],\n",
       "       [1.00000000e+01, 4.80000000e+01, 1.21167870e-01, 2.00000000e+00],\n",
       "       [9.00000000e+00, 3.40000000e+01, 1.31632184e-01, 2.00000000e+00],\n",
       "       [0.00000000e+00, 1.70000000e+01, 1.31632184e-01, 2.00000000e+00]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z = linkage(features_standardized, 'ward')\n",
    "Z[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:38:48.338649Z",
     "start_time": "2018-12-27T18:38:48.324808Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 149 entries, 1 to 149\n",
      "Data columns (total 4 columns):\n",
      "cluster_1    149 non-null int64\n",
      "cluster_2    149 non-null int64\n",
      "distance     149 non-null float64\n",
      "n_objects    149 non-null int64\n",
      "dtypes: float64(1), int64(3)\n",
      "memory usage: 4.7 KB\n"
     ]
    }
   ],
   "source": [
    "linkage_matrix = pd.DataFrame(data=Z, \n",
    "                              columns=['cluster_1', 'cluster_2', \n",
    "                                       'distance', 'n_objects'],\n",
    "                              index=range(1, n))\n",
    "for col in ['cluster_1', 'cluster_2', 'n_objects']:\n",
    "    linkage_matrix[col] = linkage_matrix[col].astype(int)\n",
    "linkage_matrix.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:38:48.350012Z",
     "start_time": "2018-12-27T18:38:48.341373Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cluster_1</th>\n",
       "      <th>cluster_2</th>\n",
       "      <th>distance</th>\n",
       "      <th>n_objects</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>101</td>\n",
       "      <td>142</td>\n",
       "      <td>0.00</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>39</td>\n",
       "      <td>0.12</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>10</td>\n",
       "      <td>48</td>\n",
       "      <td>0.12</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9</td>\n",
       "      <td>34</td>\n",
       "      <td>0.13</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>0.13</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   cluster_1  cluster_2  distance  n_objects\n",
       "1        101        142      0.00          2\n",
       "2          7         39      0.12          2\n",
       "3         10         48      0.12          2\n",
       "4          9         34      0.13          2\n",
       "5          0         17      0.13          2"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linkage_matrix.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:38:48.580888Z",
     "start_time": "2018-12-27T18:38:48.351455Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linkage_matrix[['distance', 'n_objects']].plot(secondary_y=['distance'], \n",
    "                        title='Agglomerative Clustering Progression');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Compare linkage types"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hierarchical clustering provides insight into degrees of similarity among observations as it continues to merge data. A significant change in the similarity metric from one merge to the next suggests a natural clustering existed prior to this point. \n",
    "The dendrogram visualizes the successive merges as a binary tree, displaying the individual data points as leaves and the final merge as the root of the tree. It also shows how the similarity monotonically decreases from bottom to top. Hence, it is natural to select a clustering by cutting the dendrogram. \n",
    "\n",
    "The following figure illustrates the dendrogram for the classic Iris dataset with four classes and three features using the four different distance metrics introduced above. It evaluates the fit of the hierarchical clustering using the cophenetic correlation coefficient that compares the pairwise distances among points and the cluster similarity metric at which a pairwise merge occurred. A coefficient of 1 implies that closer points always merge earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:38:48.585876Z",
     "start_time": "2018-12-27T18:38:48.581917Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "methods = ['single', 'complete', 'average', 'ward']\n",
    "pairwise_distance = pdist(features_standardized)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:39:53.703176Z",
     "start_time": "2018-12-27T18:39:49.737388Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(figsize=(15, 8), nrows=2, ncols=2, sharex=True)\n",
    "axes = axes.flatten()\n",
    "for i, method in enumerate(methods):\n",
    "    Z = linkage(features_standardized, method)\n",
    "    c, coph_dists = cophenet(Z, pairwise_distance)\n",
    "    dendrogram(Z, labels=data.label.values,\n",
    "        orientation='top', leaf_rotation=0., \n",
    "        leaf_font_size=8., ax = axes[i])\n",
    "    axes[i].set_title('Method: {} | Correlation: {:.2f}'.format(\n",
    "                                                method.capitalize(), c))\n",
    "    \n",
    "fig.tight_layout()\n",
    "fig.savefig('dendrogram', dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Different linkage methods produce different dendrogram ‘looks’ so that we can not use this visualization to compare results across methods. In addition, the Ward method that minimizes the within-cluster variance may not properly reflect the change in variance but the total variance that may be misleading. Instead, other quality metrics like the cophenetic correlation or measures like inertia if aligned with the overall goal are more appropriate. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Get Cluster Members"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:39:55.712143Z",
     "start_time": "2018-12-27T18:39:55.700083Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "n = len(Z)\n",
    "from collections import OrderedDict\n",
    "clusters = OrderedDict()\n",
    "\n",
    "for i, row in enumerate(Z, 1):\n",
    "    cluster = []\n",
    "    for c in row[:2]:\n",
    "        if c <= n:\n",
    "            cluster.append(int(c))\n",
    "        else:\n",
    "            cluster += clusters[int(c)]\n",
    "    clusters[n+i] = cluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:39:55.729283Z",
     "start_time": "2018-12-27T18:39:55.715941Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[144, 124, 120, 143]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clusters[230]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Animate Agglomerative Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:39:55.736421Z",
     "start_time": "2018-12-27T18:39:55.730923Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def get_2D_coordinates():\n",
    "    points = pd.DataFrame(features_2D).assign(n=1)\n",
    "    return dict(enumerate(points.values.tolist()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:39:55.751781Z",
     "start_time": "2018-12-27T18:39:55.738008Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "n_clusters = Z.shape[0]\n",
    "points = get_2D_coordinates()\n",
    "cluster_states = {0: get_2D_coordinates()}\n",
    "\n",
    "for i, cluster in enumerate(Z[:, :2], 1):\n",
    "    cluster_state = dict(cluster_states[i-1])\n",
    "    merged_points = np.array([cluster_state.pop(c) for c in cluster])\n",
    "    cluster_size = merged_points[:, 2]\n",
    "    new_point = np.average(merged_points[:, :2], \n",
    "                           axis=0, weights=cluster_size).tolist()\n",
    "    new_point.append(cluster_size.sum())\n",
    "    cluster_state[n_clusters+i] = new_point\n",
    "    cluster_states[i] = cluster_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:39:55.766287Z",
     "start_time": "2018-12-27T18:39:55.753970Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{15: [-2.2622145316010216, 2.686284485110592, 1.0],\n",
       " 41: [-1.8581224563735717, -2.337415157553348, 1.0],\n",
       " 60: [-0.11019628000062932, -2.6540728185365645, 1.0],\n",
       " 62: [0.5621083064431792, -1.7647243806169446, 1.0],\n",
       " 106: [0.36701768786072436, -1.5615028914765063, 1.0],\n",
       " 108: [2.006686467676607, -0.7114386535471587, 1.0],\n",
       " 109: [2.2597773490125017, 1.9210103764598867, 1.0],\n",
       " 114: [1.4676452010173247, -0.44227158737708266, 1.0],\n",
       " 176: [0.28711522075373114, -0.24204262329732348, 2.0],\n",
       " 179: [-2.2058211672986987, -0.09844552008358048, 2.0],\n",
       " 185: [0.9688104990917799, 0.01907915384081543, 3.0],\n",
       " 194: [0.7389335833626245, 0.6838170188840107, 2.0],\n",
       " 197: [2.3691965862739517, 0.33967500639352843, 2.0],\n",
       " 198: [-2.4657912495858, -0.9936714816693262, 3.0],\n",
       " 205: [1.9290326043911596, 0.5634757376107679, 3.0],\n",
       " 206: [-1.9303546578375999, 0.4980362956076001, 3.0],\n",
       " 208: [-2.3324410024278306, 0.10599232941089061, 3.0],\n",
       " 209: [2.365628354573734, 2.5914923595139356, 2.0],\n",
       " 210: [-2.3753778947842483, -0.428476399606261, 5.0],\n",
       " 211: [2.775321891622194, 0.8286062652623241, 2.0],\n",
       " 212: [1.3703381593353579, -0.4066353802439459, 3.0],\n",
       " 214: [1.4771264049002877, 0.6845006301068535, 2.0],\n",
       " 215: [0.6124063740956357, -0.11263115492758463, 4.0],\n",
       " 217: [-2.107918266740138, -0.5961767325807753, 7.0],\n",
       " 218: [-2.2074608511148277, 0.39185352432566406, 7.0],\n",
       " 219: [-2.530562663777726, 1.9721518667486764, 2.0],\n",
       " 222: [-1.9447561950630023, 0.26668291555609785, 3.0],\n",
       " 224: [1.1317839552605031, -0.7225792577873079, 2.0],\n",
       " 225: [0.17415501993333077, -0.9041186723104582, 4.0],\n",
       " 226: [1.9804041815154314, 0.5524627673500003, 3.0],\n",
       " 228: [0.5970487156101139, -0.2629983547610023, 4.0],\n",
       " 229: [1.5978708558106194, 0.9834189460574745, 3.0],\n",
       " 230: [1.944288880741274, 0.9602696562701191, 4.0],\n",
       " 231: [1.066723936158902, 0.6275964565840024, 4.0],\n",
       " 232: [-0.43239104859121186, -1.8051529981646477, 3.0],\n",
       " 233: [1.3993792903437394, -0.9150062688479023, 2.0],\n",
       " 236: [0.20202521219193983, -1.5042170574230862, 5.0],\n",
       " 237: [1.1777972305328468, -1.5706593008861836, 3.0],\n",
       " 238: [1.9089871295906673, 0.7850341610197987, 2.0],\n",
       " 239: [-2.5638395941372223, 0.5658239416152503, 3.0],\n",
       " 240: [0.5834108821437097, 0.6210769014326585, 2.0],\n",
       " 241: [1.8396217867683873, -0.02362196158643326, 3.0],\n",
       " 242: [1.4274899699312786, 0.24628913465740437, 5.0],\n",
       " 243: [0.19303006787186602, -1.003259039619637, 3.0],\n",
       " 244: [3.1041735373340296, 0.2157110044581378, 2.0],\n",
       " 245: [0.16678817742501761, -0.402792363931369, 6.0],\n",
       " 246: [-2.2446551194172795, 1.0593800316735267, 6.0],\n",
       " 247: [1.1384647649646227, -0.7829411177202094, 4.0],\n",
       " 248: [-2.0951328107676597, 1.5594656985593047, 4.0],\n",
       " 249: [1.049661370014735, -0.05911604365815985, 5.0]}"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cluster_states[100]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Set up Animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:39:55.862472Z",
     "start_time": "2018-12-27T18:39:55.767217Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "fig, ax = plt.subplots()\n",
    "xmin, ymin = np.min(features_2D, axis=0) * 1.1\n",
    "xmax, ymax = np.max(features_2D, axis=0) * 1.1\n",
    "ax.set(xlim=(xmin, xmax), ylim=(ymin, ymax))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:39:58.788933Z",
     "start_time": "2018-12-27T18:39:55.863410Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
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       "AAJsc3RzegAAAAAAAAAAAAAAlgAAO5EAAAMuAAAAHwAAABkAAAAbAAADSgAAACMAAAAaAAAAGwAA\n",
       "AwsAAAAgAAAAGAAAABgAAAEAAAADrQAAAGkAAAAcAAAAGQAAAxwAAAAkAAAAFgAAAB0AAAO/AAAA\n",
       "KQAAABoAAAAZAAACSgAAABsAAAJGAAAAHAAABBEAAAAqAAAAGwAAAB4AAAJLAAAAHAAABKIAAAAs\n",
       "AAAAGwAAAB0AAAObAAAAXwAAABoAAAAaAAAD6QAAACoAAAAZAAAAGQAAA3UAAAAjAAAAHAAAABkA\n",
       "AAOsAAAAJQAAABkAAAAZAAAEZAAAACEAAAAbAAAAFwAABFsAAAAnAAAAHQAAAB4AAAPrAAAAbwAA\n",
       "ABkAAAAbAAAGrQAAACcAAAAdAAAAHQAABKMAAAArAAAAHAAAABkAAAT5AAAANAAAABwAAAAkAAAE\n",
       "1AAAADYAAAChAAAAGgAABPYAAAAuAAAAHQAAACIAAAQ7AAAANAAAABkAAAAeAAAESgAAAEoAAAAa\n",
       "AAAAIgAABfEAAAAvAAAAHAAAABsAAAahAAAALQAAAB4AAAAdAAAHuQAAAHwAAAAfAAAAHwAABiMA\n",
       "AAAzAAAAJgAAACAAAAddAAAAOQAAACkAAAAcAAAJBAAAADEAAAAnAAAAIgAAB7AAAAAyAAAAKgAA\n",
       "ACEAAAs9AAABYQAAACYAAAApAAALrQAAADgAAAAnAAAAKAAAC4MAAABAAAAALAAAACYAAAOCAAAJ\n",
       "zAAAAxMAAAA2AAASrgAAAP8AAAHZAAAAMwAAFo0AAAVGAAAAOgAAAEUAAA8AAAAQDgAAABRzdGNv\n",
       "AAAAAAAAAAEAAAAsAAAAYnVkdGEAAABabWV0YQAAAAAAAAAhaGRscgAAAAAAAAAAbWRpcmFwcGwA\n",
       "AAAAAAAAAAAAAAAtaWxzdAAAACWpdG9vAAAAHWRhdGEAAAABAAAAAExhdmY1OC4yMC4xMDA=\n",
       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scat = ax.scatter([], [])\n",
    "def animate(i):\n",
    "    df = pd.DataFrame(cluster_states[i]).values.T\n",
    "    scat.set_offsets(df[:, :2])\n",
    "    scat.set_sizes((df[:, 2] * 2) ** 2)\n",
    "    return scat,\n",
    "    \n",
    "anim = FuncAnimation(\n",
    "    fig, animate, frames=cluster_states.keys(), interval=250, blit=False)\n",
    "HTML(anim.to_html5_video())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Scikit-Learn implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:39:58.947891Z",
     "start_time": "2018-12-27T18:39:58.789983Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/stefan/.pyenv/versions/miniconda3-latest/envs/ml4t/lib/python3.7/site-packages/sklearn/metrics/cluster/supervised.py:732: FutureWarning: The behavior of AMI will change in version 0.22. To match the behavior of 'v_measure_score', AMI will use average_method='arithmetic' by default.\n",
      "  FutureWarning)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "clusterer = AgglomerativeClustering(n_clusters=3)\n",
    "data['clusters'] = clusterer.fit_predict(features_standardized)\n",
    "fig, axes = plt.subplots(ncols=2)\n",
    "labels, clusters = data.label, data.clusters\n",
    "mi = adjusted_mutual_info_score(labels, clusters)\n",
    "axes[0].scatter(*features_2D.T, c=data.label, s=10)\n",
    "axes[0].set_title('Original Data')\n",
    "axes[1].scatter(*features_2D.T, c=data.clusters, s=10)\n",
    "axes[1].set_title('Clusters | MI={:.2f}'.format(mi))\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Comparing Mutual Information for different Linkage Options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:39:59.040554Z",
     "start_time": "2018-12-27T18:39:58.948926Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/stefan/.pyenv/versions/miniconda3-latest/envs/ml4t/lib/python3.7/site-packages/sklearn/metrics/cluster/supervised.py:732: FutureWarning: The behavior of AMI will change in version 0.22. To match the behavior of 'v_measure_score', AMI will use average_method='arithmetic' by default.\n",
      "  FutureWarning)\n",
      "/home/stefan/.pyenv/versions/miniconda3-latest/envs/ml4t/lib/python3.7/site-packages/sklearn/metrics/cluster/supervised.py:732: FutureWarning: The behavior of AMI will change in version 0.22. To match the behavior of 'v_measure_score', AMI will use average_method='arithmetic' by default.\n",
      "  FutureWarning)\n",
      "/home/stefan/.pyenv/versions/miniconda3-latest/envs/ml4t/lib/python3.7/site-packages/sklearn/metrics/cluster/supervised.py:732: FutureWarning: The behavior of AMI will change in version 0.22. To match the behavior of 'v_measure_score', AMI will use average_method='arithmetic' by default.\n",
      "  FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mutual_info = {}\n",
    "for linkage_method in ['ward', 'complete', 'average']: \n",
    "    clusterer = AgglomerativeClustering(n_clusters=3, linkage=linkage_method)\n",
    "    clusters = clusterer.fit_predict(features_standardized)  \n",
    "    mutual_info[linkage_method] = adjusted_mutual_info_score(clusters, labels)\n",
    "fig, ax = plt.subplots()\n",
    "pd.Series(mutual_info).sort_values().plot.barh()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Strengths and Weaknesses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The strengths of hierarchical clustering include that \n",
    "- you do not need to specify the number of clusters but instead offers insight about potential clustering by means of an intuitive visualization. \n",
    "- It produces a hierarchy of clusters that can serve as a taxonomy. \n",
    "- It can be combined with k-means to reduce the number of items at the start of the agglomerative process.\n",
    "\n",
    "The weaknesses include \n",
    "- the high cost in terms of computation and memory because of the numerous similarity matrix updates.\n",
    "- Another downside is that all merges are final so that it does not achieve the global optimum. - \n",
    "- Furthermore, the curse of dimensionality leads to difficulties with noisy, high-dimensional data."
   ]
  }
 ],
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